Theorem 3exp2 1169

Description: Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Hypothesis

Ref	Expression
3exp2.1	⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → τ)

Assertion

Ref	Expression
3exp2	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem 3exp2

Step	Hyp	Ref	Expression
1		3exp2.1	. . 3 ⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → τ)
2	1	ex 423	. 2 ⊢ (φ → ((ψ ∧ χ ∧ θ) → τ))
3	2	3expd 1168	1 ⊢ (φ → (ψ → (χ → (θ → τ))))

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  3anassrs  1173  ralrimivvva  2708  sfinltfin  4536